Difference between revisions of "2021 AMC 12B Problems/Problem 4"
(Created page with "The 2021 AMC 12B will be held on February 10th, 2021. The problems will not be made public until 24 hours after that.") |
Sugar rush (talk | contribs) |
||
| Line 1: | Line 1: | ||
| − | The | + | ==Problem== |
| + | Ms. Blackwell gives an exam to two classes. The mean of the scores of the students in the morning class is <math>84</math>, and the afternoon class's mean score is <math>70</math>. The ratio of the number of students in the morning class to the number of students in the afternoon class is <math>\frac{3}{4}</math>. What is the mean of the scores of all the students? | ||
| + | |||
| + | <math>\textbf{(A)} ~74 \qquad\textbf{(B)} ~75 \qquad\textbf{(C)} ~76 \qquad\textbf{(D)} ~77 \qquad\textbf{(E)} ~78</math> | ||
| + | |||
| + | ==Solution== | ||
| + | WLOG assume there <math>3</math> students in the morning class and <math>4</math> in the afternoon class. Then the average is <math>\frac{3\cdot 84 + 4\cdot 70}{7}=\boxed{\textbf{(C)} ~76}</math> | ||
Revision as of 17:39, 11 February 2021
Problem
Ms. Blackwell gives an exam to two classes. The mean of the scores of the students in the morning class is 
, and the afternoon class's mean score is 
. The ratio of the number of students in the morning class to the number of students in the afternoon class is 
. What is the mean of the scores of all the students?
Solution
WLOG assume there 
students in the morning class and 
in the afternoon class. Then the average is 
